Renormalons in Electromagnetic Annihilation Decays of Quarkonium

We study the large-order asymptotic behavior of the perturbation series for short-distance coefficients in the NRQCD factorization formulas for the decays J/ψ → e+e− and ηc → γγ. The short-distance coefficients of the leading matrix elements are calculated to all orders in the large-Nf limit. We find that there is a universal Borel resummable renormalon associated with the cancellation of the Coulomb singularity in the short-distance coefficients. We demonstrate that the ambiguities in the short-distance coefficients from the first infrared renormalon are canceled by ambiguities in the nonperturbative NRQCD matrix elements that contribute through relative order v2. Our results are used to estimate the coefficients of higher order radiative corrections in the decay rates for J/ψ → e+e−, ηc → γγ, and J/ψ → γγγ. Typeset using REVTEX